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Finding the Third Proportional to 65,142 and 97,698

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Solution

The third proportional to 65,142 and 97,698 is: 146,524.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    65,142 : 97,698 = 97,698 : x
  2. Step 2: Convert to fraction form
    65,142/97,698 = 97,698/x
  3. Step 3: Cross multiply
    65,142x = 97,698 × 97,698
  4. Step 4: Simplify right side
    65,142x = 9,544,899,204
  5. Step 5: Solve for x
    x = 9,544,899,204/65,142
  6. Step 6: Final answer
    x = 146,524.50

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.